As stated in Introduction, the stochastic differential formulation of recursive utility was introduced by Duffie and Epstein [1]}, which is actually a stochastic recursive control system. In this section, based on the connection between SDU and BSDE, we present an example to illustrate the application of our study. It should be pointed out that the inspiration of the model comes from Ivanov–Swishchuk [2]}, and for completeness, we would like to present the model in details.
